JIPMAT 2025 (QA) - Two ships are sailing in the sea on the two sides of a lighthouse. The angles of elevation of the top of the lighthouse as observed from two ships are 30° and 45°, respectively. If the lighthouse is 100 m high, the distance between two ships is approximately: | PYQs + Solutions

JIPMAT 2025

Geometry

Trigonometry

Easy

Two ships are sailing in the sea on the two sides of a lighthouse. The angles of elevation of the top of the lighthouse as observed from two ships are 30° and 45°, respectively. If the lighthouse is 100 m high, the distance between two ships is approximately:

173 m

200 m

273 m

300 m

✅ Correct Option: 3

Let Ship A and Ship B have the angle of elevation

45^\circ

and

30^\circ

, respectively.

Let their distance from the lighthouse be

x

and

y

respectively.

We know, height of lighthouse

= 100

meters

For

x

\newline

\tan (45^\circ) = \frac{Opposite side}{Adjacent Side}

\newline

1= \frac{100}{x}

\newline

x = 100

meters

For

y

\newline

\tan (30^\circ) = \frac{Opposite side}{Adjacent Side}

\newline

\frac{1}{\sqrt3}= \frac{100}{y}

\newline

y = 100\times \sqrt3

\newline

y = 100\times 1.732

\newline

y = 173.2

meters

Hence, distance between the two ships

= x + y = 100 + 173 = 273

meters.

Thus, the correct option is Option 3.

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JIPMAT 2025 (QA) PYQs

Two ships are sailing in the sea on the two sides of a lighthouse. The angles of elevation of the top of the lighthouse as observed from two ships are 30° and 45°, respectively. If the lighthouse is 100 m high, the distance between two ships is approximately:

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